The area of the stretched triangle is four times the area of the original triangle
What is a Triangle?
A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let's assume that the original triangle has sides of length a, b, and c, and that its area is A. Without loss of generality, we can assume that side a is the shortest side.
After the rubber is stretched, each side of the enlarged triangle will be twice the length of its original length. Thus, the lengths of the sides of the stretched triangle will be 2a, 2b, and 2c.
Since the rubber is stretched equally from all sides, we know that each angle of the original triangle will be doubled. Therefore, the stretched triangle will be similar to the original triangle.
The area of a triangle is given by the formula:
A = (1/2) x base x height
where the base and height are the lengths of any two sides of the triangle that are perpendicular to each other.
Since the stretched triangle is similar to the original triangle, we can use the ratios of corresponding sides to find the lengths of the corresponding altitudes. Specifically, we have:
(altitude of stretched triangle corresponding to side 2a) = 2 x (altitude of original triangle corresponding to side a)
(altitude of stretched triangle corresponding to side 2b) = 2 x (altitude of original triangle corresponding to side b)
(altitude of stretched triangle corresponding to side 2c) = 2 x (altitude of original triangle corresponding to side c)
Therefore, the area of the stretched triangle is given by:
A' = (1/2) x (2a) x (2b) x (2/2) + (1/2) x (2b) x (2c) x (2/2) + (1/2) x (2c) x (2a) x (2/2)
Simplifying this expression gives:
A' = 4A
Hence , the area of the stretched triangle is four times the area of the original triangle.
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what is 5.93^-5 in standard form?
5.93 * 10^(-5) Hope this Helps
0000593
thats the answer
Help ASAP!!!!
Fill in blank A I got B
First answer and correct answer gets the brain...
You multiply by 1.12 to find your answer
Answer: 1.12
To get this answer, you would represent 12% as 0.12 (move the decimal point 2 spots to the left to go from 12.0% to 0.12) then you add on 1 to get 1+0.12 = 1.12
Another way to think about it is to have 100% + 12% = 112%, so the new price is 112% of the old price. For example, if the car was $100 and you increase the price by 12%, then it jumps to $112. Notice how 1.12*(old price) = 1.12*100 = 112 = new price
6. Given the following equation y = 35x - 1600, write a real-life problem about a gym that could be modeled by this equation. Remember to identify your variables.
Givens
The cost of one piece of new equipment = 400
The number of new items needed = 4
Cost of one month's use = 35 dollars.
Income from 1 month's use = y
Number of members = x
Problem
Robert, the owner of a gym on the coast of Louisiana, has to replace 4 machines after a hurricane came through. Each machine costs 400. The gym cannot operate without these 4 machines. The gym will be be down for 1 month. He has x members who each pay 35 dollars for the use of the gym for a month. What is the total amount (y), that he is "out" for the month.
y = 35x + 400*4.
3x+5x
2n-3n
4c+c-7c
4x-6x+x-5x
3a+2a+7a-5
3x + 5x = 8x
2n - 3n = - n
4c + c - 7c = 5c - 7c = - 2c
4x - 6x + x - 5x = - 2x + x - 5x = - x - 5x = - 6x
3a + 2a + 7a - 5 = 5a + 7a - 5 = 12a - 5
solve the equation 5=1/2 v-3
v=?
Lines are L and M are parallel. Find m<1
George had $235 in his checking account he withdrew $20 each day on Monday Tuesday and Wednesday George got paid on Friday and deposited $130 into his checking account then on Saturday he wrote two checks one for a $167 and one for $212 what was the checking balance after writing the checks
235$ and if you withdraw 20$ on three days thats 60$ so if we remove that from the account we have 175$ left.
Then on Friday when he got paid he put 130$ into the bank he has 175+130=305$
If he wrote a check 1 for 167$ and 1 for 212$ thats his account balance - 212 then -167 = 305 -378 so he has a balance of -73
The checking balance after writing the checks is -$74.
Explanation:To calculate the checking balance after writing the checks, we need to keep track of George's transactions:
Starting balance: $235Monday: Withdraw $20 (-$20)Tuesday: Withdraw $20 (-$40)Wednesday: Withdraw $20 (-$60)Friday: Deposit $130 (+$70)Saturday: Write a check for $167 (-$97)Saturday: Write a check for $212 (-$309)To find the final balance, we add the positive values (deposits) and subtract the negative values (withdrawals and checks):
Starting balance ($235) + Deposits ($130) - Withdrawals ($60) - Checks ($167 + $212) = $235 + $130 - $60 - $167 - $212 = -$74
Therefore, the checking balance after writing the checks is -$74.
The Yu family and the Sainz family went on vacation together and each family leased a car. The leasing company charged a flat rental fee for the week, plus a charge for each mile driven. The Yu's drove 222 miles; their car cost $110.30 for the week. The Sainz's drove 147 miles; their car cost $99.05. What is the linear equation that represents the cost of a rental car? Round to the nearest hundredth
Answer:
y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Step-by-step explanation:
Given that the leasing company charged a flat rental fee for the week, plus a charge for each mile driven.
Let flat rental fee be c and cost per mile driven = m and miles driven = x
Total cost =y
Then y = mx+C is the linear equation.
to find m and c, we use the fact that y =110.30 when x = 222
i.e. 110.30 = c+222x
and similarly 99.05 = c+147x
Subtract to eliminate c
11.25 = 75 x
0.15 =x
Substitute in I equation
110.30 = c+222(0.15)
c = 77
Hence y = 0.15x+77 is the equation linear connecting total cost y and miles driven x
Answer:
y = 0.15x+77
Step-by-step explanation:
1) The minimum thickness of Saturns A ring is one-tenth kilometer. Write this decimal using a negative exponent.
2) 1/4 with negative exponent
3) 1/44 with a negative exponent
Answer:
1)[tex]10^{-1}[/tex]
2)[tex]2^{-2}[/tex]
3)[tex]12^{-2}[/tex]
Step-by-step explanation:
Using negative exponent rule:
1) one -tenth of kilometer =.1 =[tex]\frac{1}{10}=10^{-1}[/tex]
Using negative exponent rule:
2) [tex]\frac{1}{4} =\frac{1}{2^{2} }=2^{-2}[/tex]
Using negative exponent rule:
3)[tex]\frac{1}{144} =\frac{1}{12^{2} }= 12^{-2}[/tex]
Drag and drop the number to match the division problem to its quotient.
−85 ÷ 5 ________
17 -27 27 -17 13 -13
Here is you're answer:
In order to solve this equation you have to remember that a negative divided by a positive is a negative then just solve the equation.
[tex]-85 \div 5[/tex][tex]-85 \div 5 = -17[/tex][tex]= -17[/tex]Therefore you're answer is "-17."
Hope this helps!
David wants to fill his backyard swimming pool. His garden hose delivers 40 gallons in 5 minutes. How many gallons of water will be in the pool after 20 minutes? After 1 hour?
If 3 · N = 1, then N is the _____.
additive inverse
additive identity
multiplicative inverse
multiplicative identity
ANSWER
Multiplicative Inverse
EXPLANATION
If we multiply any number by its multiplicative inverse, the result is 1.
So for the given equation
[tex]3\times N=1[/tex]
[tex]N[/tex] is the multiplicative inverse of [tex]3[/tex]. That is why the result is [tex]1[/tex]
Answer:
C. Multiplicative inverse.
Step-by-step explanation:
We have been given an equation [tex]3\cdot N=1[/tex]. We are asked to find the name of N.
We can see that N is multiplied by 3 and the result is 1.
We know that a number is known as multiplicative inverse of another number, when the product of both numbers equal to 1.
Since product of 3 and N is 1, therefore, N is multiplicative inverse for our given equation.
Complete each number pattern
8,625 8,725 ______ ______ 9,024
862 962 _____ 1,162 ______
6,215 _____ 6,015 _______ ______
why shouldn't you let a doctor put one of those sticks in your mouth
just because they are scary
if you have a strong gag reflex. You also might get splinters from the stick so you should avoid it.
An apparel company uses a trucking service to deliver products from its warehouse to its retail outlets. For a one-way trip, the trucking company charges a flat rate of $250 per truck, plus $1.25 for every mile driven. The apparel company has a budget of less than $950 per trip. The apparel company’s owner wants to find out which retail outlets can be serviced with the given requirements.
Represent this situation in an inequality.
Answer:
The inequality will be: [tex]x<560[/tex] , where [tex]x[/tex] is the distance of the retail outlets from the warehouse.
Step-by-step explanation:
For a one-way trip, the trucking company charges a flat rate of $250 per truck, plus $1.25 for every mile driven.
Suppose, the number of miles driven is [tex]x[/tex]
So, the charge for [tex]x[/tex] miles will be: [tex]\$1.25x[/tex]
and the total charge for a one-way trip will be: [tex]\$250+\$1.25x[/tex]
Given that, the apparel company has a budget of less than $950 per trip.
So, the inequality will be.........
[tex]250+1.25x<950\\ \\ 1.25x<950-250\\ \\ 1.25x<700\\ \\ x<\frac{700}{1.25}\\ \\ x< 560[/tex]
Thus, the retail outlets which are less than 560 miles away from warehouse can be serviced with the given requirements.
Which graph represents the function? h(x)={ x if x<−1 −x if x≥−1 15 POINTS
Please answer quickly!! 15 points
Answer:
Option B
Step-by-step explanation:
h(x) = x if x < -1
-x if x ≥ -1
Here piece wise function is given.
Firstly we graph the line h(x) = x .
Remember that, this line start from x = -1 to -infinite , because x is less than -1.
Here we can not include the point x=-1. This situation represent with the help of circle at x = -1.
Now we graph the line h(x) = -x .
Remember that, this line start from x = -1 to infinite , because x is greater than equal to -1.
Here we include the point x=-1. This situation represent with the help of solid circle at x = -1..
So, option 2 is correct answer.
C is directly proportional to d such that c=1.5d.
find c when D=12: First you have to plug in the number so if d=12 the you do c=12(1.5) which equals 18. C=18
Find d if C=15: you now have to do the inverse operation. if c=d1.5 then d= c/1.5 Then plug in the numbers again, d=15/1.5 it equals 10, so d=10
I hope this helps (:
Question 5(Multiple Choice Worth 4 points) The legs of a right triangle are 12 centimetres and 16 centimeters. What is the length of the hypotenuse? 15 centimeters 17 centimeters 20 centimeters 28 centimeters
For this type of question, you have to use the Pythagorean Theorem:
[tex]a^{2} +b^{2} = c^{2}[/tex]
In the theorem, a and b are the legs. To find the length of the hypotenuse, you have to square the lengths of the two legs and add it together. Then, find the square root of the sum.
First square both numbers.
[tex]a=12 \\ a^{2} = 12 \times 12 = 144[/tex]
[tex]b = 16 \\b^{2} = 16 \times 16 = 256[/tex]
Now that you have the numbers, you need to add them.
[tex]144+256=400[/tex]
Now you need to find the square root of 400 to find the length of the htypotenuse.
[tex]\sqrt{400} = 20[/tex]
The length of the hypotenuse is 20 cm, which is the 3rd choice
a. 15 cm x
b. 17 cm x
c. 20 cm ✔
d. 28 cm x
If you have any questions, feel free to ask in the comments! :)
Answer:
the answer is C
Step-by-step explanation:
What is 87.252 dividend by 2.2 I am not sure how to do the work
Answer:
39.66
Step-by-step explanation:
If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.
Divide like you usually do
Put decimal point directly above decimal point in the dividend.
Check your answer.
Answer:
39.66
Hope this helps :-)
ten times the sum of half a number and 6 is 8
10(1/2x + 6) = 8
Distributive property.
5x + 60 = 8
Subtract 60 from both sides.
5x = -52
Divide both sides by 5.
x = -10.4 (This is your answer.)
y=3x−7
Complete the missing value in the solution to the equation.
(1,___)
I beleive the answer = (1, -4)
Answer:
Step-by-step explanation:
y= 3x-7= -4x
Draw a model, and write an equation to represent "4 times as many as 3 is 12." Explain your work.
The equation [tex]4 * 3 = 12[/tex] is an accurate mathematical representation of the statement. First, create a model using objects, such as circles or blocks, to represent the numbers involved:-
Now,
Draw three circles to represent the number 3.
Then, draw four groups of three circles each, representing "4 times as many as 3."
In total, you will have 12 circles.
Now, write an equation to describe this model:-
[tex]4 * 3 = 12[/tex]
In this equation:-
The number 4 represents the "4 times as many as" part of the statement.
The number 3 represents the initial quantity, which is multiplied.
The result, 12, represents the total or the final amount.
The equation [tex]4 * 3 = 12[/tex] is an accurate mathematical representation of the statement. It shows that when you multiply 3 by 4, you indeed get 12, which aligns with the given statement that "4 times as many as 3 is 12." This visual and algebraic representation helps to understand and demonstrate the concept of multiplication.
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The volume of a cylindrical soap dispenser is modeled by the expression below.select the true statement.a. the expression (x + 1)2 represents the height of the soap dispenser.b. the expression (x + 1)2 represents the radius of the soap dispenser.c. the factor 4x + 1 represents the height of the soap dispenser.d. the factor 4x + 1 represents the area of the base of the soap dispenser.
Answer:
The expression [tex](x+1)^2[/tex] represents the radius of the soap dispenser.
The expression [tex]4x+1[/tex] represents the height of the soap dispenser.
Step-by-step explanation:
The question says that the soap dispenser is in the form of a cylinder.
Now, we find the volume of the cylinder by using the given formula:
[tex]V= \pi r^2 h[/tex], where V represents the volume, 'r' represents the radius, and 'h' represents the height of the cylinder.
Now, the volume is the product of radius squared and the height, if they both are functions of [tex]x[/tex], then the function to represent the volume must have cubic exponents.
Since, the radius is squared in the formula and it is a function of [tex]x[/tex] that implies that the function of radius must have square as the exponent of [tex]x[/tex], therefore, the expression [tex](x+1)^2[/tex] will represent the radius of the soap dispenser and the expression [tex](4x+1)[/tex] represents the height of the soap dispenser.
Answer:
D
Step-by-step explanation:
7719 equal 83×93 explain why 83×93 is not the prime factorization of 7719
Answer:
7719 = 3*31 * 83
Step-by-step explanation:
Because 93 can be factored down further. It is 31*3. So the prime factorization of
7719: 83 * 31 * 3
83 is a prime. It cannot be broken down any further.
In August Emily’s clothing store sold 460 shirts with the ration of short sleeve to long sleeve being 3:7. How many short sleeve shirts where sold?
Emily's clothing store sold 138 short sleeve shirts, calculated by dividing the total shirts by the sum of the ratio parts (10) and multiplying the result by the short sleeve part of the ratio (3).
The question asks how many short sleeve shirts were sold if the ratio of short sleeve to long sleeve shirts is 3:7 and a total of 460 shirts were sold. To find the answer, first calculate the total parts of the ratio by adding both parts of the ratio together, which is 3+7=10.
Then, divide the total number of shirts by the total parts of the ratio to find out how many shirts each part of the ratio represents: 460/10=46. Since the ratio of short sleeve shirts is 3 parts, multiply the number each part represents by 3 to get the number of short sleeve shirts: 46*3=138. Therefore, Emily's clothing store sold 138 short sleeve shirts.
Think about converting 48% to an equivalent fraction in reduced form. If the denominator is 25, what is the numerator?
Answer:
the numerator is 12
Step-by-step explanation:
since 48 is a percent, it would be put as 48/100 as a fraction. since both the numerator and denominator are divisible by 4, you can reduce the fraction into 12/25. Since the question is asking what the numerator was when the denominator was 25, the answer is 12.
Answer:
A=12
Step-by-step explanation:
5 smoothies in each batch.hom many smoothie did she make today
Is there any more info?
factorise y^2 - 16
(y squared)
[tex]y^2-16=y^2-4^2=(y-4)(y+4)\\\\\text{used}\ a^2-b^2=(a-b)(a+b)[/tex]
Solve For in P in the scientific formula PV=nRT
To solve this problem you must apply the proccedure shown below:
1. You have the following formula given in the problem above:
[tex]PV=nRT[/tex]
3. Then, to solve for P you only need to move V from the left member to the right member. V is multiplying P, therefore, it will divide [tex]nRT[/tex], as you can see below:
[tex]PV=nRT\\P=\frac{nRT}{V}[/tex]
Therefore, the answer is: [tex]P=\frac{nRT}{V}[/tex]
What is -4(7x+5)=-160
Answer is -23
Add 4 from both sides
Subtract 5 from both sides
Then divide 7
To get rid of the parantheses we must multiply -4 times anything inside the parantheses.
-4(7x+5)=-160
-28x-20=-160
Add 20 to both sides of the equation.
-28x-20=-160
-28x=-140
Divide both sides by -28
-28x/-28=-140/-28
x=5
Our final answer is 5
Hope this helps!